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I ran the following Quadratic regression. I want to report my findings, and I want to include the DFs for x and x^2. Can I assume they are 55? (2+53). The R output is not very clear on this. Sorry, I know it's a basic question but I just wanted some confirmation. 

lm(formula = y ~ x + x2)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.67303 -0.13330 -0.00798  0.11700  0.84015 
   Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.1395     0.2049  15.325  < 2e-16 ***
x             2.4679     0.6627   3.724 0.000476 ***
x2           -1.3211     0.4410  -2.995 0.004160 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
   Residual standard error: 0.2869 on 53 degrees of freedom
Multiple R-squared:  0.377, Adjusted R-squared:  0.3535 
F-statistic: 16.03 on 2 and 53 DF,  p-value: 3.585e-06

So to clarify, I want to report this in the following way, but was wondering if 55 is correct:

(R^2 =.38, F(2,53)=16.03, p<.001), where X significantly predicts Y (\beta = .47, t(55) = 4.28, p<.001), as does X^2 (\beta = -.32, t(55) = -3.00, p<.01).

dorien
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    Since the R output very specifically states 2 and 53 DF on the last line, which looks very clear indeed, could you explain what you mean by "DFs for $x$ and $x^2$"? – whuber Aug 22 '16 at 21:40
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    I know it says that for the model. I was wondering if I could report DF for each variable separately, like so: (R^2 =.38, F(2,53)=16.03, p<.001), where X significantly predicts Y (\beta = .47, t(55) = 4.28, p<.001), as does X^2 (\beta = -.32, t(55) = -3.00, p<.01). – dorien Aug 22 '16 at 21:43
  • Any ideas anybody if I should report those and what they are? – dorien Aug 24 '16 at 14:29

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